A study of an arbitrary unsteady Stokes flow in and around a liquid sphere

An arbitrary unsteady Stokes flow past a liquid sphere is considered. The representation of velocity and pressure in an arbitrary unsteady Stokes flow proposed by Venkatalaxmi et al. (2004) [22,23] was employed in this study by assuming the shape of the liquid drop to be spherical as a first approximation. The surface equation of the deformed sphere has been determined by an iterative method up to the first order approximation by taking surface tension into account (Landau and Lifshitz, 1978) [8]. The flow inside a liquid sphere which is generated due to an arbitrary singularity has also been studied by a similar method. The deformed interfaces in both the external and internal cases have been illustrated by examples.